论文标题
两速模型的指数收敛到平衡，该模型通过分解估计值具有变化的漂移场
Exponential convergence to equilibrium for a two-speed model with variant drift fields via the resolvent estimate
论文作者
论文摘要
我们研究了具有变化磁场的两速模型，该模型概括了Goldstein-Taylor模型，但两个对流场不一定是成比例的。由于缺乏稳态的局部均衡结构，因此不可直接应用于这种系统。为了证明该模型的指数收敛到平衡，我们使用GearhartPrüss定理的最新概括[SCI。中国数学。 64（2021），否。 3，507-518]为了获得半群界，其中相对熵估计在通过紧凑型参数获得所需的分解估计中起着核心作用。
We study a two-speed model with variant drift fields, which generalizes the Goldstein-Taylor model but the two advection fields are not necessarily in proportion. Due to the lack of a local equilibrium structure of the steady state, prevailing hypocoercivity methods could not be directly applied to such a system. To prove the exponential convergence to equilibrium for this model, we use a recent generalization of the Gearhart-Prüss theorem [Sci. China Math. 64 (2021), no. 3, 507-518] to gain semigroup bounds, where the relative entropy estimate plays a central role in gaining desired resolvent estimates via a compactness argument.
